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Finding the Third Proportional to 4,196 and 6,178

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Solution

The third proportional to 4,196 and 6,178 is: 9,096.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,196 : 6,178 = 6,178 : x
  2. Step 2: Convert to fraction form
    4,196/6,178 = 6,178/x
  3. Step 3: Cross multiply
    4,196x = 6,178 × 6,178
  4. Step 4: Simplify right side
    4,196x = 38,167,684
  5. Step 5: Solve for x
    x = 38,167,684/4,196
  6. Step 6: Final answer
    x = 9,096.21

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.